Question

Enter the first usable host on the network 12.48.105.97 255.255.252.0.

Please show work.

Answer 1

12.48.104.1

Explanation:
-------------
IP Address: 12.48.105.97
----------------------------------------
Let's first convert this into binary format
12.48.105.97
Let's convert all octets to binary separately
Converting 12 to binary
Divide 12 successively by 2 until the quotient is 0
   > 12/2 = 6, remainder is 0
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1100
So, 12 of decimal is 1100 in binary
12 in binary is 00001100

Converting 48 to binary
Divide 48 successively by 2 until the quotient is 0
   > 48/2 = 24, remainder is 0
   > 24/2 = 12, remainder is 0
   > 12/2 = 6, remainder is 0
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 110000
So, 48 of decimal is 110000 in binary
48 in binary is 00110000

Converting 105 to binary
Divide 105 successively by 2 until the quotient is 0
   > 105/2 = 52, remainder is 1
   > 52/2 = 26, remainder is 0
   > 26/2 = 13, remainder is 0
   > 13/2 = 6, remainder is 1
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1101001
So, 105 of decimal is 1101001 in binary
105 in binary is 01101001

Converting 97 to binary
Divide 97 successively by 2 until the quotient is 0
   > 97/2 = 48, remainder is 1
   > 48/2 = 24, remainder is 0
   > 24/2 = 12, remainder is 0
   > 12/2 = 6, remainder is 0
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1100001
So, 97 of decimal is 1100001 in binary
97 in binary is 01100001

===================================================================================
||    12.48.105.97 in binary notation is 00001100.00110000.01101001.01100001    ||
===================================================================================

Subnet address: 255.255.252.0
----------------------------------------
Let's convert this into binary format
255.255.252.0
Let's convert all octets to binary separately
Converting 255 to binary
Divide 255 successively by 2 until the quotient is 0
   > 255/2 = 127, remainder is 1
   > 127/2 = 63, remainder is 1
   > 63/2 = 31, remainder is 1
   > 31/2 = 15, remainder is 1
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11111111
So, 255 of decimal is 11111111 in binary
255 in binary is 11111111

Converting 255 to binary
Divide 255 successively by 2 until the quotient is 0
   > 255/2 = 127, remainder is 1
   > 127/2 = 63, remainder is 1
   > 63/2 = 31, remainder is 1
   > 31/2 = 15, remainder is 1
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11111111
So, 255 of decimal is 11111111 in binary
255 in binary is 11111111

Converting 252 to binary
Divide 252 successively by 2 until the quotient is 0
   > 252/2 = 126, remainder is 0
   > 126/2 = 63, remainder is 0
   > 63/2 = 31, remainder is 1
   > 31/2 = 15, remainder is 1
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11111100
So, 252 of decimal is 11111100 in binary
252 in binary is 11111100

Converting 0 to binary
Divide 0 successively by 2 until the quotient is 0
Read remainders from the bottom to top as 
So, 0 of decimal is  in binary
0 in binary is 00000000

====================================================================================
||    255.255.252.0 in binary notation is 11111111.11111111.11111100.00000000    ||
====================================================================================

Remove all dots to form 11111111111111111111110000000000
Remove all 0's from the right side to form 1111111111111111111111
Number of 1's in this is 22
so, Subnet mask is /22

For Calculating network ID, keep first 22 bits of 00001100.00110000.01101001.01100001 and set all remaining bits to 0.
so, network ID in binary is 00001100.00110000.01101000.00000000
00001100.00110000.01101000.00000000:
----------------------------------------
00001100.00110000.01101000.00000000
Let's convert all octets to decimal separately
Converting 00001100 to decimal
Converting 00001100 to decimal
00001100
=> 0x2^7+0x2^6+0x2^5+0x2^4+1x2^3+1x2^2+0x2^1+0x2^0
=> 0x128+0x64+0x32+0x16+1x8+1x4+0x2+0x1
=> 0+0+0+0+8+4+0+0
=> 12
00001100 in decimal is 12

Converting 00110000 to decimal
Converting 00110000 to decimal
00110000
=> 0x2^7+0x2^6+1x2^5+1x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+0x64+1x32+1x16+0x8+0x4+0x2+0x1
=> 0+0+32+16+0+0+0+0
=> 48
00110000 in decimal is 48

Converting 01101000 to decimal
Converting 01101000 to decimal
01101000
=> 0x2^7+1x2^6+1x2^5+0x2^4+1x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+1x64+1x32+0x16+1x8+0x4+0x2+0x1
=> 0+64+32+0+8+0+0+0
=> 104
01101000 in decimal is 104

Converting 00000000 to decimal
Converting 00000000 to decimal
00000000
=> 0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+0x64+0x32+0x16+0x8+0x4+0x2+0x1
=> 0+0+0+0+0+0+0+0
=> 0
00000000 in decimal is 0

===================================================================================
||    00001100.00110000.01101000.00000000 in decimal notation is 12.48.104.0    ||
===================================================================================
==========================================
||    So, Network ID is 12.48.104.0    ||
==========================================

For Calculating first valid address in subnet, add 1 to the network address.
Network Address is 12.48.104.0
=============================================================
||    So, first valid address in subnet is 12.48.104.1    ||
=============================================================